Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

22 Fluid Mechanics, Thermodynamics of Turbomachinery
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Problems
1. A fan operating at 1750 rev/min at a volume flow rate of 4.25 m 3 /s develops a head of 153
mm measured on a water-filled U-tube manometer. It is required to build a larger, geometrically
similar fan which will deliver the same head at the same efficiency as the existing fan, but at a
speed of 1440 rev/min. Calculate the volume flow rate of the larger fan.
2. An axial flow fan 1.83 m diameter is designed to run at a speed of 1400 rev/min with an
average axial air velocity of 12.2 m/s. A quarter scale model has been built to obtain a check on
the design and the rotational speed of the model fan is 4200 rev/min. Determine the axial air
velocity of the model so that dynamical similarity with the full-scale fan is preserved. The effects
of Reynolds number change may be neglected.
A sufficiently large pressure vessel becomes available in which the complete model can be
placed and tested under conditions of complete similarity. The viscosity of the air is independent
of pressure and the temperature is maintained constant. At what pressure must the model be tested?
3. A water turbine is to be designed to produce 27 MW when running at 93.7 rev/min under
a head of 16.5 m. A model turbine with an output of 37.5 kW is to be tested under dynamically
similar conditions with a head of 4.9 m. Calculate the model speed and scale ratio. Assuming a
model efficiency of 88%, estimate the volume flow rate through the model.
It is estimated that the force on the thrust bearing of the full-size machine will be 7.0 GN. For
what thrust must the model bearing be designed?
4. Derive the non-dimensional groups that are normally used in the testing of gas turbines
and compressors.
A compressor has been designed for normal atmospheric conditions (101.3 kPa and 15°C). In
order to economise on the power required it is being tested with a throttle in the entry duct to